Children show large individual differences in numerical skills, even before they begin formal education. These early differences have significant and long-lasting effects, with numerical knowledge before school predicting mathematical achievement throughout the primary and secondary school years. Currently, little is known about the dispositional factors influencing children's numerical development. Why do some children engage with and succeed in mathematics from an early age, whilst others avoid mathematics and struggle to acquire even basic symbolic number skills?
This thesis examines the role of two dispositional factors: First, spontaneous focusing on numerosity (SFON), a recently developed construct which refers to an individual's tendency to focus on the numerical aspects of their environment; and second, mathematics anxiety (MA), a phenomenon long recognised by educators and researchers but one which is relatively unexplored in young children. These factors are found to have independent effects on children's numerical skills, thus the empirical work is presented in two separate parts.
The SFON studies start by addressing methodological issues. It is shown that the current measures used to assess children's SFON vary in their psychometric properties and subsequently a new and reliable picture-based task is introduced. Next, the studies turn to theoretical questions, investigating the causes, consequences and mechanisms of SFON. The findings give rise to three main conclusions. First, children's SFON shows little influence from parental SFON and home numeracy factors. Second, high SFON children show a symbolic number advantage. Third, the relationship between SFON and arithmetic can be explained, in part, by individual differences in children's ability to map between nonsymbolic and symbolic representations of number.
The MA studies focus primarily on gender issues. The results reveal no significant differences between boys' and girls' overall levels of MA; however, there are gender differences in the correlates of MA. Specifically, boys' (but not girls') MA is related to parents' MA. Moreover, the relationship between MA and mathematical outcomes is stronger for boys than it is for girls. Possible causal explanations for these gender differences are explored in two ways: First, by examining the reliability of the scales used to assess MA in boys and girls. Second, by investigating the relationship between girls' (and boys') mathematics anxiety and their societal math-gender stereotypes.
The findings from both sets of studies draw a link between children's emerging dispositions towards mathematics and their early numerical skills. Future research needs to examine how these dispositional factors interact with other (cognitive and non-cognitive) predictors of mathematics achievement.

Description:

A Doctoral Thesis. Submitted in partial fulfilment of the requirements for the award of Doctor of Philosophy of Loughborough University.